Ballet Folklórico de México
This is probably Mexico's most accomplished dance company and academy, which performs classic, regional dances from all over the country both in Mexico city and abroad. The performances are super colorful, if a little kitschy, visual feasts that are great to take kids to: Part of the fun is checking out all the regional costumes from traditional indigenous outfits to Mariachi ensembles. Founded by ballerina and choreographer Amalia Hernandez in the late 1950's, her legacy continues to this day, with several performances a week at Bellas Artes. In December and January, they also perform in the evenings outside of Chapultepec Castle, which makes for a fun holiday activity.
Museo Mural Diego Rivera
Balderas y Colón, Centro Histórico
While it's host to temporary exhibitions on contemporary artists and muralists, the whole point of visiting this teensy museum is to see one of Diego Rivera's most famous murals, Dream of a Sunday Afternoon in the Alameda Central, which survived the building that housed it in the 1985 earthquake that ravaged the city. Like in many of his murals, it's a Marxist critique of the upper-echelons of the ruling class, and history buffs get their kicks from trying to identify all the historical figures he painted in, Frida included. Located in the Centro Histórico, it's a quick, easy stop on a full day of sightseeing in the area.
Palacio de Bellas Artes
Av. Juárez, Centro Histórico
The Adamo Boari-designed, Beaux Arts palace is the crown jewel of the Centro Histórico with impressive marble interiors and massive murals by practically every major national muralist from Diego Rivera, to David Alfaro Siqueiros, to Rufino Tamayo. There's usually a worthwhile visiting art exhibition here, though the real highlight is catching a performance in the theater, which boasts a glass Tiffany curtain designed by the famed landscape artist Dr. Atl.
Plaza de la Constitución, Centro Historico
Built on the site of the last Aztec emperor's home, this enormous Palace was once the home of Hernan Cortes, the Spanish conquistador, and has been the seat of Mexican government since gaining independence from Spain. While there are tours of the palace's architecture and a few galleries dedicated to the 19th-century president Benito Juarez, the real highlight is Diego Rivera's massive mural representing the entire history of the Mexican people from its indigenous origins, to the Spanish conquest, to the arrival of Marxist ideology—Rivera was an ardent communist. Like many of his murals, it's a historical who's who. The Palace is sometimes closed to visitors, so it's worth calling ahead.
Seminario 8, Centro Histórico
When Hernan Cortés and his army of Spanish conquistadores arrived in México city—then Tenochtitlan—they raised the Aztec capital, destroyed its temples, and used many of the building materials to erect their own palaces and, famously, the Cathedral. There are few remnants left of what was once the capital of the vast Mesoamerican Empire, but the ruins of their most important temple, the Templo Mayor, which is located right next to the Zócalo, were discovered in the late '70s and have been open to visitors ever since. The site is an active archaeological dig, with some pretty impressive ancient frescoes, and an on-site museum displaying the thousands of ancient artefacts—elaborate offerings made for the gods—discovered here over the years.
Museo de Arte Popular
Revillagigedo 11, Centro Histórico
Housed in a beautifully restored Art Deco building in the Centro Histórico, this museum is home to Mexican folk handicrafts and textiles from around the country. It's a nicely manageable museum and a great place to bring kids, with weekend workshops that teach everything from paper maché to how to make amate paper. Don't miss the museum shop, which is one of the best places to find quality regional crafts.
Museo Franz Mayer
Av. Hidalgo 45, Centro Histórico
Franz Mayer was a German immigrant who lived in Mexico in the early 20th-century and amassed an enormous collection of decorative arts—everything from silver, to furnishings from the 16th-century on, to talavera tiles and pottery made in Puebla. Although he did acquire pieces in Europe and around the world, much of his collection was made in Mexico, and visiting the museum is a window into the elegant and elaborate furniture, paintings, and decorations that decorated the upper crust's homes during the colonial period. Upon his death, he left his collection and a generous trust to the Banco de Mexico, which opened the museum to the public in the '80s in an elegant, restored 16th-century ex-monastery. Aside from Mayer's inheritance, the museum continues to acquire special pieces and collections, and puts on great contemporary design exhibitions, too.
Museo Memoria y Tolerancia
Plaza Juarez, Centro Histórico
With a focus on human rights atrocities around the world, from an extensive exhibition on the Holocaust, to Darfur, Armenia, and Guatemala, this intelligently designed museum encourages empathy, tolerance, and commitment. After witnessing the devastation and horrors that have occurred around the world, visitors (literally) see a ray of light, and enter a room where they're encouraged to make a choice between ambivalence and committing to take action. All in all, it's actually an uplifting experience. In a country not unfamiliar with human rights abuse, this fantastic museum is making an important case for tolerance. Having partnered with Sesame Street (Plaza Sesamo), they've also developed an outstanding curriculum for kids which includes activities around bullying, a rampant problem in Mexican schools these days.
Zinco Jazz Club
Motolinia 20, Centro Histórico
All the major jazz acts that come through the city book at least one night here, which is why more often than not, the Zinco makes for a solid evening's entertainment. Aside from the good music, this spot oozes retro charm. Hidden away in the Centro, on the bottom floor of a restored Art Deco bank building, the small space feels like an authentic old New York jazz bar with crimson velvet curtains, a few intimate club tables, and a long bar serving up old school cocktails.
Isabel La Católica #30, Centro Histórico
If there's one designer who has managed to take traditional Mexican embroidery and textile techniques and make them contemporary and wearable—and not in a hippie-ish way—it's Carla Fernández. She's spent years traveling the country establishing partnerships with some of the best indigenous artisans to make her bold, geometric designs. The clothing rails at her shop at the Downtown Hotel were designed by Pedro Reyes, one of the most prominent conceptual artists in Mexico—a great match for Carla and her smart, sustainable clothing line.